Liverpool's owners are due in England on Tuesday to advance their search for a new manager and, according to the Wigan Athletic chairman, Dave Whelan, will have only 48 hours to decide whether Roberto Martínez is the man to succeed the sacked Kenny Dalglish.

John W Henry, Liverpool's principal owner, is scheduled to hold a second round of talks with the Wigan manager upon the Spaniard's return from holiday in Barbados. The pair met in Miami last Thursday for what Whelan described as "constructive talks" but, contrary to claims from the Wigan chairman, no formal offer was made to Martínez by Liverpool.

Henry and Tom Werner, the Liverpool chairman, always intended to sound out several candidates for the managerial vacancy before holding further talks this week. Martínez is not the only manager they wish to meet and, though a second official approach has not been made to Swansea City regarding Brendan Rodgers, the 39-year-old remains of interest to the Liverpool hierarchy.

Rodgers rejected Liverpool's approach for an interview shortly after Dalglish was fired and has no wish to be part of a "beauty parade" for the job. Liverpool are hopeful his stance will change by his presence on their shortlist, although the Swansea chairman, Huw Jenkins, dismissed reports of a planned meeting as "pure speculation".

Swansea also released a statement that read: "We would like to clarify the speculation in the press surrounding our manager Brendan Rodgers. We would like to confirm that there has been no contact from Liverpool and nothing has changed since our previous statement on the issue."

Henry and Werner have no plans to meet the former Liverpool manager Rafael Benítez at present, while their interest in André Villas-Boas has cooled over the past week.

Whoever is appointed as Liverpool's manager will have to accept working alongside a sporting director-type figure and Fenway Sports Group, the club's owner, has earmarked Louis van Gaal for that position. Van Gaal, however, may yet ask to be considered for the manager's role.

Despite criticism of the process of finding Dalglish's successor, and the deadline set by Whelan on Martínez, FSG will not be pressured into a critical decision in its running of Liverpool.

Whelan initially gave Liverpool and Aston Villa, who are also keen on Martínez, until 5 June to reach agreement with his manager but the deadline has now been brought forward.

"Roberto has told me he is speaking with Liverpool again on Tuesday," said Whelan. "I have now made it clear that I want this sorted out by Thursday at the latest as we have to get on preparing for next season."

Wigan have no plans to hold a press conference about Martínez's future on Tuesday and Whelan claims Liverpool's interest in the Swansea manager illustrates they have no chosen successor to Dalglish in mind.

The Wigan chairman added: "If it is true that Liverpool want to speak with Brendan Rodgers, it proves they don't know who they want as manager. I hope they choose Brendan Rodgers."